Find a basis for each of these subspaces of R*: (a) All vectors whose components are equal. (b) All vectors whose components add to zero. (c) All vectors that are perpendicular to (1,1,0,0) and (1,0, 1, 1). (d) The column space and the nullspace of I (4 by 4).

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.5: Basis And Dimension
Problem 65E: Find a basis for the vector space of all 33 diagonal matrices. What is the dimension of this vector...
icon
Related questions
Question
16
Find a basis for each of these subspaces of R4:
(a) All vectors whose components are equal.
(b) All vectors whose components add to zero.
(c) All vectors that are perpendicular to (1,1,0,0) and (1,0, 1, 1).
(d) The column space and the nullspace of I (4 by 4).
Transcribed Image Text:16 Find a basis for each of these subspaces of R4: (a) All vectors whose components are equal. (b) All vectors whose components add to zero. (c) All vectors that are perpendicular to (1,1,0,0) and (1,0, 1, 1). (d) The column space and the nullspace of I (4 by 4).
Expert Solution
steps

Step by step

Solved in 3 steps with 5 images

Blurred answer
Recommended textbooks for you
Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning